#inelastic collision

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According to repetition definition, it is a process of iteration to approach a desired goal or result or target. During the repetition process each process is called an “iteration” and output of each iteration is used to find next iteration. In mathematics, this process is basically used in functions to find the next values of particular function where each output value works as input for next iteration.

It is used to check the behavior of complex functions by getting values at regular interval of time. Collatz Conjecture and Juggler Sequence are some of the problem where we mainly use the repetition process or iteration process. It is the repeated application for any process or function to minimize the complexity. There are lots of other problems like patterns in polynomials, candy for everyone, integer iterations on a circle, Mandelbrot and Julia sets, newton's method and the cantor set where we use repetition. To understand that more deeply we take an example of the Mandelbrot set. In this we have a function x2 + c where we denote x0 for real or complex number. By applying the function x0 we get the new number as:

x1 = (x0)2 + c

Now iterate the output result of previous computation then,

x2 = (x1)2 + c

Similarly we again iterate the output result of previous computation then

x3 = (x2)2 + c

Again we iterate the output result

x4 = (x3)2 + c

and finally we take another iteration,

x5 = (x4)2 + c

  In this process following outcomes which we get after the iteration are x0, x1, x2, x3, x4 and x5. We can also say that it is the orbit of x0 under the iteration of function x2 + c.